Question 29.10: A discrete random variable has probability distribution x 1 ......
A discrete random variable has probability distribution
Calculate
(a) the expected value
(b) the standard deviation
| x | 1 | 2 | 3 | 4 | 5 |
| P(x) | 0.12 | 0.15 | 0.23 | 0.3 | 0.2 |
Step-by-Step
(a) \mu=\sum x_{i}p_{i} = 1(0.12) + 2(0.15) + 3(0.23) + 4(0.3) + 5(0.2) = 3.31
(b) \sigma^{2}=\sum p_{i}(x_{i}-\mu)^{2}
= 0.12(1 − 3.31)² + 0.15(2 − 3.31)² + 0.23(3 − 3.31)²
+0.3(4 − 3.31)² + 0.2(5 − 3.31)²
= 1.6339
standard deviation = \sigma=\sqrt{1.6339}=1.278
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